if 10 different balls are to placed in 4 distinct balls at random,then the probability that two of these boxes contain exactly 2 and 3 balls is:
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Answered by
1
Total ways to distribute 10 balls in 4 boxes is = 4¹⁰
Total ways of placing exactly 2 and 3 balls in any two of these boxes is
= ⁴C2 × ¹⁰C5× (5!/(2!3!)) × 2 × 2⁵
P(E) = 945/2¹⁰
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Answered by
1
Given:
Total number of balls = 10
Random placement = 4
To Find:
Probability that two of these boxes contain exactly 2 and 3 balls
Solution:
Two boxes can be selected in ways = 4C2
Total ways in which two boxes will consist of exactly two and these balls
= 4C2 x 10C2 x 8C2 x 2`5 x 2!
Now,
Total ways of distributing 10 balls in four boxes = 4`10
Thus,
The required probability = 4C2 x 10C2 x 8C2 x 2`5 x 2!/ 4`10
= 12/2 x 90/2 x 56x12/2 x 2`5 x 2/ 4`10
= 3 x 45 x 7 x 2`5/2`15
= 945/2`10
Answer: Probability that two of these boxes contain exactly 2 and 3 balls is 945/2`10
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